**How** to define characteristics of Impedance in Transmission line?

**How**to define characteristics of Impedance in Transmission line?

*Components of transmission line include wire , coaxial cables, dielectric slabs, optical fibre, electric power lines and Wave guides.*

*Transmission line can represented**In terms of four distributed parameters:*

*I) R = Resistance per unit length*

*II) L = Inductance per unit length** *

*III) G = Conductance per unit length*

*IV) C = Capacitance per unit length*

*Characteristics Impedance :-*

It is defined as ratio of positively traveling voltage wave to current wave at any point online. It is also known as natural impedance.

Characteristics Impedance,

√ R + j2Ï€fL

Z0 = -------------------- ohms

√ G + j2Ï€fC

Propagation constant of line,

Gamma (Î³)= (

**Î± ) Alpha**+ j(

**Î²) beta**

Here

**Î±**is real of propagation constant and it's measure of changes in magnitude Of current or Voltage in each section and is called attenuation constant. And

**Î²**is an

Imaginary part of propagation and is the difference in phase angle between the input Current and the output Current or the corresponding voltage and is called phase shift constant.

Gamma(Î³) =√ ZY = √ ( R + j2Ï€fL ) ( G + j2Ï€fC)

Phase velocity of propagation,

2Ï€

Vp =

**Î»**f = --------

**Î² ( beta)**

2Ï€

And wavelength

**Î»**= -------

**Î²**

Characteristics impedance is fixed by the geometry of two conductors. For a parallel wire line with insulation, it is

276 d

Calculated as Z0 = ---------- log e ----

√k r

Where d = Distance between conductor

Centres

r = Radius of Conductor

k = Relative permittivity of

Insulation between Conductors

For a coaxial transmission line, The characteristics Impedance is calculated as

138 d1

Z0 = --------- log e ------

√k d2

Where d1 = Inside diameter of outer

Conductor

d2 = Outside diameter of inner

Conductor

Velocity factor of cable,

Velocity of wave propagation

= ----------------------------------------------

Velocity of light in vacuum

v 1

= ----- = ------

c √k

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